Cyclotron resonance in coronal holes:: 1.: Heating and acceleration of protons, O5+, and Mg9+

The resonant heating and acceleration of protons and selected heavy ions in coronal holes are investigated by calculating trajectories of individual test particles under the influence of gravity, the electrostatic electric field, the mirror force, and the resonant acceleration due to interaction with dispersive ion cyclotron waves. The transverse heating due to the resonance is also included. We show in general terms how heavy ions can be more than mass proportionally heated, emphasizing that wave dispersion may play an important part in producing very hot heavy ions. We pay particular attention to the ultraviolet coronagraph spectrometer (UVCS) SOHO observation that the transverse temperature of O5+ is still increasing out to the outer limit of observation at similar to 3.5 solar radii. Using both approximate analytical expressions and the trajectory calculations, we find that this observation can only be reproduced if the magnetic power spectrum falls off at least as steeply as k(-2), where k is wavenumber. Surprisingly, this conclusion holds even when the power spectrum consists of two power laws, if the inner scale is proportional to the proton inertial length. Once the particles are heated transversely by the resonance, the mirror force provides the dominant outward acceleration and leads to heavy ions which how faster than the protons. It is shown that it is possible to construct a model which gives reasonable agreement with the UVCS/SOHO data for both protons and O5+ Overall, we conclude that it is highly likely that the cyclotron resonance is responsible for heating protons and heavy ions in coronal holes. However, we also briefly discuss some data for Mg9+, which do not fit the overall picture.